Posted by
Toyin Akin-4 on
Oct 21, 2002; 5:14am
URL: http://quantlib.414.s1.nabble.com/RE-Delta-on-Capfloor-tp2259p2266.html
Hi again,
In addition, a cap structure being a portfolio of caplets does not include
information regarding the correlation being
the individual FRA's. You'll need to look at swaptions for this.
I may be wrong here but I wouldn't try to compare a swap's sensitivity to
that of the cap's.
The 2 numbers really account for different measures of risk.
compare swap sensitivity with that of swaptions
compare a FRA's sensitivity to that of caplet's
a series of FRA's sensitivity (which really is a swap) should thus be
compared to swaptions.
Regards,
Toy.
----- Original Message -----
From: "Toyin Akin" <
[hidden email]>
To: "Perissin Francesco" <
[hidden email]>; "'Andre Louw'"
<
[hidden email]>; "QuantlibUsers (E-mail)"
<
[hidden email]>
Sent: Monday, October 21, 2002 11:54 AM
Subject: Re: [Quantlib-users] RE:Delta on Capfloor
> Hi all,
>
> Remember, a cap is a series of caplets. thus you are buying a portfolio of
> options.
> Like any portfolio of options, the sum of the deltas, which will be your
> total sensitivity if rates move can
> be well over 1.0. However the delta of any *ONE* caplet will be <= +-
1.0.
>
> If each caplet is well in the money, then each caplet will have a delta of
> 1. Thus the sum will be above one.
>
> Also, a caplet is an option on an individual FRA. Thus you cannot really
> bring swaps into this.
> You may be confusing swaptions with caps here.
>
> A swaption is an option on a swap.
>
> Regards,
> Toyin Akin.
>
>
> ----- Original Message -----
> From: "Perissin Francesco" <
[hidden email]>
> To: "'Andre Louw'" <
[hidden email]>; "QuantlibUsers (E-mail)"
> <
[hidden email]>
> Sent: Monday, October 21, 2002 11:13 AM
> Subject: RE: [Quantlib-users] RE:Delta on Capfloor
>
>
> >
> > Hi,
> >
> > >The answer given originally to my question on calculating the delta on
a
> > >capfloor structure was that it is simply the sum of the delta's on all
> the
> > >caplets (assuming flat nominals, there is no weighting needed).
> >
> >
> > I gave you this answer assuming another definition of delta for an
> interest
> > rate instrument, i.e. the change in present value given a parallel shift
> of
> > 1bp in the used curve. Also, this is quite close to the change obtained
by
> > shifting of 1bp the prices of the benchmarks used to bootstrap the yield
> > curve.
> > This seems to be equal to what you name "sensititvity", is it right?
> >
> > Regarding the definition that you are referring to, (i.e. the cap
> > sensitivity divided by the IRS sensitivity) I have to think a while
about
> > it. The example could help.
> >
> >
> >
> > >e.g I have a 3Mx12M, 3 monthly cap, which results in 3 caplets, results
> as
> > >follows:
> > >the 1st strikes at a delta of 0.6, the 2nd strikes at a delta of 0.5,
the
> > >3rd at a delta of 0.4. Summing these gives 1.5!
> >
> >
> > Just for understanding, do you mean that the first fixing is in 3 months
> ans
> > last fixing in 9 months? Which curr? Which strike?
> > In any case, it's not correct to sum the deltas (according to your
> > definition). I would be tempted to say that you should sum the caplet
> > sensitivities in order to get the cap sensitivity. Now you could divide
> the
> > result by the IRS sensitivity, isn't it?
> > Let me know it this can help...
> >
> >
> > >Ok, maybe it's on the Delta with respect to spot: the above caplets
gives
> > >0.13, 0.11, 0.08, giving a total of 0.32, (doesn't 'feel' right!),
> > depending
> > >on the termstructure and the length of the cap, the sum of the
> spot-delta's
> > >quite often goes over 1.0!
> >
> >
> > Andre, I could not understand this... could you try to explain again the
> > above numbers?
> >
> >
> > Ciao
> > Francesco
> > --
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